摘要
随机规划问题是人们生活和工作中常见的,是各类含随机因素的管理问题的核心,也是解决各种含随机因素的管理问题的基础。在对随机优化问题进行求解时,人们常用随机变量的期望值或机会约束模型进行去随机性处理,但是,一方面随机变量的期望值不能精确地表示该随机变量,因而通过这样处理所得的解在实际情况下未必存在或最优;另一方面当随机特征复杂(即随机环境的分布形式难以确定)时,机会约束模型的计算复杂度太大,难以建立解析形式的可行的求解方案,这两方面的问题制约了随机优化问题的最佳求解问题。本课题针对随机环境下的优化方法进行研究,主要包括综合效应函数的定义及性质,随机规划综合效应函数模型的凸性讨论,规划结果的优化问题等。
首先,针对单目标随机规划问题,提出了综合效应函数的概念,并利用目标函数和约束条件的融合问题,建立了基于综合效应函数的随机规划模型,并在此基础上分析了其可操作性问题;其次,针对多目标随机规划问题,通过引入综合效应函数的概念,建立了基于综合效应函数的多目标随机规划模型,并对规划结果的优越性进行分析;再次,对一类特殊的随机规划问题进行了凸性问题讨论,提出了随机凸与随机凹的概念,讨论了随机凸与随机凹的相关性质,进而在分析随机规划的本质特征基础上,建立了一类基于综合效应函数的随机规划模型问题的求解方法;文章中结合实例进一步分析了该模型的特点和有效性。
The stochastic programming is widely existed in our job and life, is a core of kind of manage course with random factors, and is also the basis for resolving management issues with random factors. When solve the stochastic optimization problems, it is generally used to get rid of the randomicity through the expectation of random variable or the chance- constrained model. But, on the one hand, the expectation of a random variable cannot represent the random variable accurately, so the solution got by using the the expectation model may not be existed or the optimal solution; on the other hand, when the stochastic characteristics are complex (that is to say, it is difficult to determine the distribution of the stochastic environment), the computational complexities of the chance-constrained model is so large to get an analytic form of the programming viable solution. In this paper, we consider a new way to solve stochastic, including the definition and properties of synthesizing effect function, the convexity of the synthesizing effect function model for stochastic programming, the optimization of programming solutions.
Firstly, for the stochastic programming problem, we propose the concept of synthesizing effect function, and give the stochastic programming model based on the synthesizing effect function by processing objective function and constraints, and analyze the reliability; secondly, for the multi-objective stochastic programming problem, we use the concept of multi-attribute synthesizing effect function, give the multi-objective stochastic programming models based on the synthesizing effect function, and analyze the ascendency of results; thirdly, for solving a special stochastic programming problem, we propose the concept of stochastic convexity and stochastic concavity, and discuss the properties of stochastic convexity and stochastic concavity; further, based on analyzed the basic characteristics of stochastic programming problems, we establish a general solution model based on synthesizing effect function for stochastic programming problem; in the paper, we analyze the characteristic of our model by an example, and the results indicate that our methods are effective.
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